Praise be to Allah.
If someone swears that he will not go back to a particular sin, then he goes back to it, then he swears the same oath regarding the same sin repeatedly before offering expiation for breaking his oath, then he has to offer one expiation, even if he swore the oath repeatedly.
But if he had offered expiation for his first oath, then it happened a second time and he swore a second oath to give it up, then in this case he must offer another expiation. This has been discussed previously in the answer to question no. 103424 ; please see this question for more information.
But if he swore oaths regarding different things, and broke these oaths, then he must offer expiation for each matter concerning which he swore an oath, even if he swore many oaths.
For more information on expiation for breaking an oath (kaffaarat al-yameen), please see the answer to question no. 45676 .
If what you have to do is offer a single expiation, based on the details mentioned above, then there is no reason why you cannot combine offering expiation for the oath and doing ‘umrah, because offering a single expiation does not usually have an impact on one’s wealth, especially for one who is able to save money for the purpose of travelling. So he will not be unable to offer expiation by feeding ten poor persons or clothing them, for a single expiation.
But if there are a number of expiations, and you are not able to offer expiation for your vow, but you have enough money to do ‘umrah, then offering expiation for breaking your oath must take precedence over doing ‘umrah, because it is obligatory to offer expiation immediately, according to the view of the majority of scholars.
It says in al-Mawsoo‘ah al-Fiqhiyyah (10/14): The majority of scholars are of the view that it is not permissible to delay offering expiation for breaking an oath, and that it becomes obligatory as soon as the oath is broken, because this applies when a command is mentioned in general terms. End quote.
And because the scholars (may Allah have mercy on them) have stated that Hajj and ‘umrah are not obligatory for a person until after he has fulfilled obligatory duties, which include offering any expiations that a person owes. For more information, please see the answer to question no. 11534 .
Based on that, if you have sufficient money to feed or clothe ten poor persons, then you must offer expiation by doing that. If you do not have enough money to do that, then it is valid for you to fast in that case. For more information, please see the answer to question no. 100322 .
And Allah knows best.